Lightning represents one of the most critical issues for electrical infrastructure. In dealing wi... more Lightning represents one of the most critical issues for electrical infrastructure. In dealing with overhead distribution line systems, indirect lightning strikes can lead to induced voltages overcoming the critical flashover value of the line, thus damaging the insulators. The computation of lightning-induced voltages requires the modeling of the lightning current, the evaluation of the lightning electromagnetic fields and the solution of the field-to-line coupling equations. The numerical calculation of the lightning electromagnetic fields is time-consuming and is strongly dependent on the lightning channel modeling and soil properties. This article presents a review of the most widely adopted methods to calculate the lightning electromagnetic fields, starting from the classical formulation, which requires numerical integration, and highlighting the most effective approaches that have been developed to reduce computational effort. This is done first for the case of a perfectly con...
The linear sampling method is a fast inversion technique for visualizing the profile of a scatter... more The linear sampling method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far-field pattern. The mathematical result at the basis of this method is that, given a spatial grid of points covering the scatterer, for each grid point there is an approximate solution of a linear integral equation whose L norm blows up when the point approaches the boundary of the scatterer from inside and stays large when the point is outside the scatterer. According to a recent formulation, the linear sampling method requires the regularized solution of a single functional equation where the unique optimal value of the regularization parameter is fixed by means of the generalized discrepancy principle. Within this framework in this paper we first show that the introduction of an incompatibility measure in the generalized discrepancy function provides more reliable maps of the scatterer. Then we apply active contour techniques to the visualization maps in...
The Radon transform is a linear integral transform that mimics the data formation process in medi... more The Radon transform is a linear integral transform that mimics the data formation process in medical imaging modalities like X-ray Computerized Tomography and Positron Emission Tomography. The Hough transform is a pattern recognition technique, which is mainly used to detect straight lines in digital images and which has been recently extended to the automatic recognition of algebraic plane curves. Although defined in very different ways, in numerical applications both transforms ultimately take an image as an input and provide, as an output, a function defined on a parameter space. The parameters in this space describe a family of curves, which represent either the integration domains considered in the (generalized) Radon transform, or the curves to be detected by means of the Hough transform. In both cases, the 2D plot of the intensity values of the output function is the so-called (Radon or Hough) sinogram. While the Hough sinogram is produced by an algorithm whose implementation...
In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic i... more In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it merges a qualitative and a quantitative method to optimize the way of exploiting the a priori information on the background within the inversion procedure, thus improving the quality of the reconstruction and reducing the data amount necessary for a satisfactory result. In the qualitative step, this a priori knowledge is utilized to implement the linear sampling method in its near-field formulation for an inhomogeneous background, in order to identify the region where the scatterer is located. On the other hand, the same a priori information is also encoded in the quantitative step by extending and applying the contrast source inversion method to what we call the `inhomogeneous Lippmann-Schwinger equation': the latter is a generalization ...
In the present paper, we develop a novel Bayesian approach to the problem of estimating neural cu... more In the present paper, we develop a novel Bayesian approach to the problem of estimating neural currents in the brain from a fixed distribution of magnetic field (called topography), measured by magnetoencephalography. Differently from recent studies that describe inversion techniques, such as spatio-temporal regularization/filtering, in which neural dynamics always plays a role, we face here a purely static inverse problem. Neural currents are modelled as an unknown number of current dipoles, whose state space is described in terms of a variable--dimension model. Within the resulting Bayesian framework, we set up a sequential Monte Carlo sampler to explore the posterior distribution. An adaptation technique is employed in order to effectively balance the computational cost and the quality of the sample approximation. Then, both the number and the parameters of the unknown current dipoles are simultaneously estimated. The performance of the method is assessed by means of synthetic da...
A novel approach to neuromagnetic data analysis is presented. This technique is aimed at studying... more A novel approach to neuromagnetic data analysis is presented. This technique is aimed at studying synchronised spontaneous activity (SSA) and has been used to resolve two different signals from one single evoked response, providing evidence for two possibly distinct sources. The data presented are consistent with a model that permits the generators of spontaneous activity to be synchronised by sensory stimuli.
Abstract. In this paper we present a hybrid approach to numerically solve two-dimensional electro... more Abstract. In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is ‘hybrid ’ in that it merges a qualitative and a quantita-tive method to optimize the way of exploiting the a priori information on the background within the inversion procedure, thus improving the quality of the reconstruction and reducing the data amount necessary for a satisfactory result. In the qualitative step, this a priori knowledge is utilized to im-plement the linear sampling method in its near-field formulation for an inhomogeneous background, in order to identify the region where the scatterer is located. On the other hand, the same a priori information is also encoded in the quantitative step by extending and applying the contrast source inversion method to what we call the ‘inhomogeneous Lippmann-Schwinger equation’: the latter is a generaliza...
Lightning represents one of the most critical issues for electrical infrastructure. In dealing wi... more Lightning represents one of the most critical issues for electrical infrastructure. In dealing with overhead distribution line systems, indirect lightning strikes can lead to induced voltages overcoming the critical flashover value of the line, thus damaging the insulators. The computation of lightning-induced voltages requires the modeling of the lightning current, the evaluation of the lightning electromagnetic fields and the solution of the field-to-line coupling equations. The numerical calculation of the lightning electromagnetic fields is time-consuming and is strongly dependent on the lightning channel modeling and soil properties. This article presents a review of the most widely adopted methods to calculate the lightning electromagnetic fields, starting from the classical formulation, which requires numerical integration, and highlighting the most effective approaches that have been developed to reduce computational effort. This is done first for the case of a perfectly con...
The linear sampling method is a fast inversion technique for visualizing the profile of a scatter... more The linear sampling method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far-field pattern. The mathematical result at the basis of this method is that, given a spatial grid of points covering the scatterer, for each grid point there is an approximate solution of a linear integral equation whose L norm blows up when the point approaches the boundary of the scatterer from inside and stays large when the point is outside the scatterer. According to a recent formulation, the linear sampling method requires the regularized solution of a single functional equation where the unique optimal value of the regularization parameter is fixed by means of the generalized discrepancy principle. Within this framework in this paper we first show that the introduction of an incompatibility measure in the generalized discrepancy function provides more reliable maps of the scatterer. Then we apply active contour techniques to the visualization maps in...
The Radon transform is a linear integral transform that mimics the data formation process in medi... more The Radon transform is a linear integral transform that mimics the data formation process in medical imaging modalities like X-ray Computerized Tomography and Positron Emission Tomography. The Hough transform is a pattern recognition technique, which is mainly used to detect straight lines in digital images and which has been recently extended to the automatic recognition of algebraic plane curves. Although defined in very different ways, in numerical applications both transforms ultimately take an image as an input and provide, as an output, a function defined on a parameter space. The parameters in this space describe a family of curves, which represent either the integration domains considered in the (generalized) Radon transform, or the curves to be detected by means of the Hough transform. In both cases, the 2D plot of the intensity values of the output function is the so-called (Radon or Hough) sinogram. While the Hough sinogram is produced by an algorithm whose implementation...
In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic i... more In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it merges a qualitative and a quantitative method to optimize the way of exploiting the a priori information on the background within the inversion procedure, thus improving the quality of the reconstruction and reducing the data amount necessary for a satisfactory result. In the qualitative step, this a priori knowledge is utilized to implement the linear sampling method in its near-field formulation for an inhomogeneous background, in order to identify the region where the scatterer is located. On the other hand, the same a priori information is also encoded in the quantitative step by extending and applying the contrast source inversion method to what we call the `inhomogeneous Lippmann-Schwinger equation': the latter is a generalization ...
In the present paper, we develop a novel Bayesian approach to the problem of estimating neural cu... more In the present paper, we develop a novel Bayesian approach to the problem of estimating neural currents in the brain from a fixed distribution of magnetic field (called topography), measured by magnetoencephalography. Differently from recent studies that describe inversion techniques, such as spatio-temporal regularization/filtering, in which neural dynamics always plays a role, we face here a purely static inverse problem. Neural currents are modelled as an unknown number of current dipoles, whose state space is described in terms of a variable--dimension model. Within the resulting Bayesian framework, we set up a sequential Monte Carlo sampler to explore the posterior distribution. An adaptation technique is employed in order to effectively balance the computational cost and the quality of the sample approximation. Then, both the number and the parameters of the unknown current dipoles are simultaneously estimated. The performance of the method is assessed by means of synthetic da...
A novel approach to neuromagnetic data analysis is presented. This technique is aimed at studying... more A novel approach to neuromagnetic data analysis is presented. This technique is aimed at studying synchronised spontaneous activity (SSA) and has been used to resolve two different signals from one single evoked response, providing evidence for two possibly distinct sources. The data presented are consistent with a model that permits the generators of spontaneous activity to be synchronised by sensory stimuli.
Abstract. In this paper we present a hybrid approach to numerically solve two-dimensional electro... more Abstract. In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is ‘hybrid ’ in that it merges a qualitative and a quantita-tive method to optimize the way of exploiting the a priori information on the background within the inversion procedure, thus improving the quality of the reconstruction and reducing the data amount necessary for a satisfactory result. In the qualitative step, this a priori knowledge is utilized to im-plement the linear sampling method in its near-field formulation for an inhomogeneous background, in order to identify the region where the scatterer is located. On the other hand, the same a priori information is also encoded in the quantitative step by extending and applying the contrast source inversion method to what we call the ‘inhomogeneous Lippmann-Schwinger equation’: the latter is a generaliza...
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Papers by Riccardo Aramini